help in binomial distribution maths a level mei

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SongYiLo
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A multiple-choice test consists of 18 questions. For each question there are four possible answers given, only one of which is correct. John does no revision for this test so decides to choose the answer to each question randomly.
can someone explain how to do this? thank you xx

(i) What is the probability that he gets no questions correct? [2]

(ii) What is the probability that he gets three questions correct? [3]

(iii) If John gets only three questions correct, what is the probability that they are the first three questions? [3]

(iv) What is the most likely number of questions that he gets right? [3]

(v) Students who get more than half the questions correct pass this test. What is the probability that John passes? [3]

(vi) After the test John reckoned that, if he had done ‘a little revision’, there were four questions which he would definitely have got correct and that he would have been able to eliminate one of the wrong answers in each of the other 14 questions, before randomly guessing his answer. Show that with ‘a little revision’ his chances of passing would have been increased by a factor of more than 50. [3]
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phillipisrael
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(i) (3/4)^18=0.0056
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ghostwalker
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(Original post by SongYiLo)
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The parts of this question are at varying levels of difficulty. I would expect you to be able to do some of them. If you truely haven't been able to do any of it, I suspect you shouldn't be looking at this question just yet.

Post your working so far.
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